Abstract During navigation, the power system components (such as propeller, transmission shaft, etc.) on the ship will generate complex vibrations due to the action of various forms of excitation force. Due to the influence of the operating condition and the change of the wake field, the excitation force cannot be accurately measured and calculated, so the excitation force has the characteristics of uncertainty. In this paper, the non-random vibration response analysis method based on the convex model of non-probabilities is presented, which is used to solve the dynamic response limit of multi-degree of freedom system under time-varying uncertain excitation, and the expression for solving the dynamic response limit is given. The Monte Carlo simulation method is used to verify the reliability of the response boundary, which is the case with fewer excitation samples Improve the robustness of the dynamic response prediction of the shafting system to provide a useful reference.